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It says that the Catholic Diocese of Christchurch knows of no surviving next of kin for Father Ginaty, Bishop Grimes, Bishop Brodie nor Bishop Joyce.
"But it must use its best endeavours to ensure that any such person is consulted," it says.
The Diocese's move to apply for disinterment comes as the cathedral on Barbadoes St is to be demolished.
The decision for the cathedral - almost 120 years old - to be demolished was finalised last year after it was badly damaged in earthquakes in 2010 and the major quake in February, 2011.
Bishop who dreamed of the cathedral more than 100 years ago among affected
Among the clergymen affected is the man who was instrumental in building the cathedral in the first place.
Bishop Grimes, appointed as the first Catholic bishop of Christchurch in 1887, received support from the Pope for the project after returning from a trip to Rome in 1899.
The cathedral foundation stone was put down in February 1901. The church officially opened in February 1905 and was regarded as one of the finest in Australasia.
The application to disinter the men is due to be lodged on Friday, August 14.
Anyone who is related to the clergymen who the Diocese has not been able to contact is encouraged to get in touch with the Diocese on (03) 366 9869 or bishops-pa@chch.catholic.org.nz.